In this paper by using the Poincaré compactification of ℝ3 we make a global analysis of the model xʹ = ax + y + yz, yʹ = x – ay + bxz, zʹ = cz – bxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values of the parameters we provide the global phase portrait of the system in the Poincaré ball. We also describe the α and ω-limit sets of its orbits in the Poincaré ball.

中文翻译：

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关于三维强制阻尼微分系统的全局动力学

本文利用ℝ3的庞加莱紧化，我们对模型xʹ=ax+y+yz，yʹ=x-ay+bxz，zʹ=cz-bxy进行全局分析。特别是我们给出了它在无穷大球体上的动力学的完整描述。对于 a + c = 0 或 b = 1，该系统具有不变量。对于这些参数值，我们提供了庞加莱球中系统的全局相图。我们还描述了庞加莱球中其轨道的 α 和 ω 极限集。